Theorem 19.23tOLD 1819

Description: Obsolete proof of 19.23t 1800 as of 1-Jan-2018. (Contributed by NM, 7-Nov-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.23tOLD	|- ( F/xps -> (A.x(ph -> ps) <-> (E.xph -> ps)))

Proof of Theorem 19.23tOLD

Step	Hyp	Ref	Expression
1		exim 1575	. . 3 |- (A.x(ph -> ps) -> (E.xph -> E.xps))
2		19.9t 1779	. . . 4 |- ( F/xps -> (E.xps <-> ps))
3	2	imbi2d 307	. . 3 |- ( F/xps -> ((E.xph -> E.xps) <-> (E.xph -> ps)))
4	1, 3	syl5ib 210	. 2 |- ( F/xps -> (A.x(ph -> ps) -> (E.xph -> ps)))
5		nfnf1 1790	. . 3 |- F/x F/xps
6		nfe1 1732	. . . . 5 |- F/xE.xph
7	6	a1i 10	. . . 4 |- ( F/xps -> F/xE.xph)
8		id 19	. . . 4 |- ( F/xps -> F/xps)
9	7, 8	nfimd 1808	. . 3 |- ( F/xps -> F/x(E.xph -> ps))
10		19.8a 1756	. . . . 5 |- (ph -> E.xph)
11	10	a1i 10	. . . 4 |- ( F/xps -> (ph -> E.xph))
12	11	imim1d 69	. . 3 |- ( F/xps -> ((E.xph -> ps) -> (ph -> ps)))
13	5, 9, 12	alrimdd 1768	. 2 |- ( F/xps -> ((E.xph -> ps) -> A.x(ph -> ps)))
14	4, 13	impbid 183	1 |- ( F/xps -> (A.x(ph -> ps) <-> (E.xph -> ps)))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540  E.wex 1541   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)